TY  - JOUR
A1  - Albus, Alexander P.
A1  - Gardiner, Simon A.
A1  - Illuminati, Fabrizio
A1  - Wilkens, Martin
T1  - Quantum field theory of dilute homogeneous Bose-Fermi-mixtures at zero temperature : general formalismand beyond mean-field corrections
N2  - We consider a dilute homogeneous mixture of bosons and spin-polarized fermions at zero temperature. We first construct the formal scheme for carrying out systematic perturbation theory in terms of single particle Green's functions. We introduce a new relevant object, the renormalized boson-fermion T-matrix which we determine to second order in the boson-fermion s-wave scattering length. We also discuss how to incorporate the usual boson-boson T-matrix in mean-field approximation to obtain the total ground state properties of the system. The next order term beyond mean- field stems from the boson-fermion interaction and is proportional to $a_{scriptsize BF}k_{scriptsize F}$. The total ground-state energy-density reads $E/V =epsilon_{scriptsize F} + epsilon_{scriptsize B} + (2pihbar^{2}a_{
m BF}n_{scriptsize B}n_{scriptsize F}/m) [1 + a_{scriptsize BF}k_{scriptsize F}f(delta)/pi]$. The first term is the kinetic energy of the free fermions, the second term is the boson-boson mean-field interaction, the pre-factor to the additional term is the usual mean-field contribution to the boson-fermion interaction energy, and the second term in the square brackets is the second-order correction, where $f(delta)$ is a known function of $delta= (m_{scriptsize B} - m_{scriptsize F})/(m_{scriptsize B} + m_{scriptsize F})$. We discuss the relevance of this new term, how it can be incorporated into existing theories of boson-fermion mixtures, and its importance in various parameter regimes, in particular considering mixtures of $^{6}$Li and $^{7}$Li and of $^{3}$He and $^{4}$He.
Y1  - 2002
UR  - http://xxx.lanl.gov/abs/cond-mat/0201102
ER  - 
TY  - JOUR
A1  - Albus, Alexander P.
A1  - Illuminati, Fabrizio
A1  - Wilkens, Martin
T1  - Ground-state properties of trapped Bose-Fermi mixtures: Role of exchange correlation
Y1  - 2003
ER  - 
TY  - JOUR
A1  - Busch, Thomas
A1  - Englert, Bertold-Georg
A1  - Rzazewski, Kazimierz
A1  - Wilkens, Martin
T1  - Two cold atoms in a harmonic trap
N2  - Two ultracold atoms moving in a trap interact weakly at a very short distance. This interaction can be modeled by a properly regularized contact potential. We solve the corresponding time-independent Schrödinger equation under the assumption of a parabolic, spherically symmetric trapping potential.
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Eisert, Jens
A1  - Felbinger, Timo
A1  - Papadopolous, P.
A1  - Plenio, M. B.
A1  - Wilkens, Martin
T1  - Classical information and distillable entanglement
N2  - We establish a quantitative connection between the amount of lost classical information about a quantum state and the concomitant loss of entanglement. Using menthods that have been developed for the optimal purification of miced states, we find a class of miced states with known distillable entanglement. These results can be used to determine the quantum capacity of a quantum channel which randomizes the order of transmitted signals.
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Eisert, Jens
A1  - Wilkens, Martin
T1  - Catlysis of Entanglement Manipulation for Mixed States
N2  - We consider entanglement-assisted remote quantum state manipulation of bipartite mixed states. Several aspects are addressed: we present a class of mixed states of rank two that can be transformed into another class of mixed states under entanglement-assisted local operations with classical communication, but for which such a transformation is impossible without assistance. Furthermore, we demonstrate enhancement of the efficiency of purification protocols with the help of entanglement-assisted operations. Finally, transformations from one mixed state to mixed target states which are sufficiently close to the source state are contrasted with similar transformations in the pure-state case.
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Eisert, Jens
A1  - Wilkens, Martin
T1  - Quantum games
N2  - In these lecture notes we investigate the implications of the identification of strategies with quantum operations in game theory beyond the results presented in [J. Eisert, M. Wilkens, and M. Lewenstein, Phys. Rev. Lett. 83, 3077 (1999)]. After introducing a general framework, we study quantum games with a classical analogue in order to flesh out the peculiarities of game theoretical settings in the quantum domain. Special emphasis is given to a detailed investigation of different sets of quantum strategies.
Y1  - 2000
UR  - http://xxx.lanl.gov/abs/quant-ph/0004076
ER  - 
TY  - JOUR
A1  - Eisert, Jens
A1  - Wilkens, Martin
A1  - Lewenstein, Maciej
T1  - Quantum Games and Quantum Strategies
N2  - We investigate the quantization of nonzero sum games. For the particular case of the Prisoners' Dilemma we show that this game ceases to pose a dilemma if quantum strategies are allowed for. We also construct a particular quantum strategy which always gives reward if played against any classical strategy.
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Felbinger, Timo
A1  - Santos, L.
A1  - Wilkens, Martin
A1  - Lewenstein, Maciej
T1  - Time Correlations of a laser-induced Bose-Einstein condensate
N2  - We analyze the multi-time correlations of a laser-induced Bose Einstein condensate. We use quantum stochastic methods to obtain under certain circumstances a Fokker-Planck equation which describes the phase-difussion process, and obtain an analytical expression of the two-time correlations. We perform also quantum Monte Carlo numerical simulations of the correlations, which are in good agreement with the predicted analytical results.
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Felbinger, Timo
A1  - Wilkens, Martin
T1  - Stochastic Wave-function Simulation of Two-time Correlation Functions
N2  - We propose an algorithm for the numerical simulation of two-time correlation functions by means of stochastic wave function. As a first application, we investigate the two-time correlation function of a nonlinear optical parametric oscillator.
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Henkel, Carsten
A1  - Poetting, Sierk
A1  - Wilkens, Martin
T1  - Loss and heating of particles in small and noisy traps
N2  - We derive the time and loss rate for a trapped atom that is coupled to fluctuating fields in the vicinity of a room-temperature metallic and/or dielectric surface. Our results indicate a clear predominance of near-field effects over ordinary blackbody radiation. We develop a theoretical framework for both charged ions and neutral atoms with and without spin. Loss processes that are due to a transition to an untrapped internal state are included.
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Henkel, Carsten
A1  - Wilkens, Martin
T1  - Heating of trapped atoms near thermal surfaces
N2  - We study the electromagnetic coupling and concomitant heating of a particle in a miniaturized trap close to a solid surface. Two dominant heating mechanisms are identified: proximity fields generated by thermally exicted currents in the absorbing solid and timedependent image potentials due to elastic surfaces distortions (Rayleigh phonons. Estimates for the lifetime of the trap ground state are given. Ions are paricularly sinsitive to electric proximity fields: for a silver substrate, we find a lifetime below one second at distrances closer than some ten 10^-6m to the surfaces. Neutral atoms may approach the surface more closely: if they have a magnetic moment, a minimum distance of one 10^-6m is estimatied in tight traps, the heat being transferred via magnetic proximity fields. For spinless atoms, heat is transferred by inelastic scattering of virtual photons off sorface phonons. The corresponding lifetime, however, is estimated to be extremely long compared to the timescale of typical experiments.
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Henkel, Carsten
A1  - Wilkens, Martin
T1  - Heating of trapped particles close to surfaces-blackbody and beyond
N2  - We discuss heating and decoherencw in traps fpr ions and neutral paricles close to metallic surfaces. We focus on simple trap geometries and compute noise spectra of thermally excited electromagnetic fields. If the trap is located in the near field of the substrate, the field fluctuations are largely increased compared to the level of the blackbody field, leading to much shorter coherence and life times of the trapped atoms. The correspinding time constants are computed for ion traps and magnetic traps. Analytical estimates for the size dependence of the noise spectrum are given. We finally discuss prospects for the coherent transport of matter waves in integrated surface waveguides.
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Idziaszek, Zbigniew
A1  - Gajda, M.
A1  - Navez, Patrick
A1  - Wilkens, Martin
A1  - Rzazewski, Kazimierz
T1  - Fluctuation of the Weakly Interacting Bose-Einstein Condensate
N2  - We consider the role of weak interaction on the fluctuations of the number of condensed atoms within canonical and microanonical ensembles. Unlike the correspinding case of the ideal gas this is not a clean, well-defined problem of mathematical physics. Two related reasons are the following: there is no unique way of defining the condensate fraction of the interacting system and no exact energy levels of the interacting system are known.
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Idziaszek, Zbigniew
A1  - Wilkens, Martin
T1  - Scattering of atoms on the Bose-Einstein condensate
N2  - We investigate the scattering of slowly moving atoms on the Bose-Einstein condensate. The condensate excitations are described by Bogolyubov-de Gennes equatins. We derive the analytic expressions for the differential cross section for both elastic and ineladtic channels. For the elastic channel we obtain analytic results for total cross sections, and discuss their scaling with the number of condensed atoms. For inelastic channels we present numerical results for the total cross section.
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Illuminati, Fabrizio
A1  - Navez, Patrick
A1  - Wilkens, Martin
T1  - Thermodynamic identities and paricle number fluctuations in weakly interacting Bose-Einstein condensates
N2  - We derive exact thermodynamic identities relating the average number of condensed atoms and the root-mean- square fluctuations determined in different statistical ensembles for the weakly interacting Bose gas confined in a box. This is achieved by introducing the concept of auxiliary partition functions for model Hamiltonians that do conserve the total number of particles. Exploiting such thermodynamic identities, we provide the first, completely analytical prediction of the microcanonical particle number fluctuations in the weakly interacting Bose gas. Such fluctuations, as a function of the volume V of the box are found to behave normally, in contrast wiht the anomalous scaling behaviour V3/ 4 of the fluctuations in the ideal Bose gas.
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Janicke, U.
A1  - Wilkens, Martin
T1  - Atomic matter wave amplification by optical pumping
N2  - The atom laser (or `Boser') is a device that delivers a beam of atomic de Broglie waves with high coherence and monochromaticity. In this review, we concentrate on an all-optical scheme of an atom laser that is based on optical pumping. The model is first presented in terms of kinetic equations, and its relation to the ordinary laser and the Bose-Einstein condensation is discussed. We then derive a master equation for the quantum statistics dynamics of the atom laser. Neglecting photon reabsorption processes, the master equation is solved and the counting statistics is computed. Finally, the effects of the inelastic reabsorption processes are investigated for the particular case of two atoms. It is shown that the onset of atom-lasing is suppressed in large resonators, but may be achieved in small and/or low-dimensional resonators.
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Javanainen, Juha
A1  - Wilkens, Martin
T1  - Phase and Phase Diffusion of a Split Bose-Einstein Condensate
N2  - We analyze theoretically an experiment in which a trapped Bose-Einstein condensate is cut in half, and the parts are subsequently allowed to interfere. If the delay cutting and atom detection is small, the interference pattern of the two halves of the condensate is the same in every experiment. However, for longer delays the spatial phase of the interference shows random fluctuations from one experiment to the other. This phase diffusion is characterized quantitatively.
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Javanainen, Juha
A1  - Wilkens, Martin
T1  - Phase and phase diffusion of a split Bose-Einstein condensate
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Leonhardt, Ulf
A1  - Wilkens, Martin
T1  - Aharonov-Bohm scattering of neutral atoms
N2  - We study the scattering of quantum particles in the presence of an Aharonov-Bohm vortex and in an arbitrary cylindrically symmetric potential. In particular we address the scattering of atoms carrying dipole moments induced by an electrically charged wire and a homogeneous magnetic field. We argue that, despite the strong attraction of the wire, an Aharoniv-Bohm effect will be visible.
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Lewenstein, Maciej
A1  - Cirauqui, David
A1  - Angel Garcia-March, Miguel
A1  - Corominas, Guillem Guigo
A1  - Grzybowski, Przemyslaw
A1  - Saavedra, Jose R. M.
A1  - Wilkens, Martin
A1  - Wehr, Jan
T1  - Haake-Lewenstein-Wilkens approach to spin-glasses revisited
JF  - Journal of physics : A, Mathematical and theoretical
N2  - We revisit the Haake-Lewenstein-Wilkens approach to Edwards-Anderson (EA) model of Ising spin glass (SG) (Haake et al 1985 Phys. Rev. Lett. 55 2606). This approach consists in evaluation and analysis of the probability distribution of configurations of two replicas of the system, averaged over quenched disorder. This probability distribution generates squares of thermal copies of spin variables from the two copies of the systems, averaged over disorder, that is the terms that enter the standard definition of the original EA order parameter, qEA 0 0
KW  - Edwards-Anderson order parameter
KW  - Haake-Lewenstein-Wilkens approach
KW  - spin glass
KW  - Saddle Point
KW  - Steppest Descend method
Y1  - 2022
U6  - https://doi.org/10.1088/1751-8121/ac9d10
SN  - 1751-8113
SN  - 1751-8121
VL  - 55
IS  - 45
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Navez, Patrick
A1  - Wilkens, Martin
T1  - Single molecule in a Bose-Einstein condensate
N2  - We study a model describing a rotating linear rigid molicule interacting with a Bose-Einstein condensate. A generalization of the Landau criterion is established and gives the limit for which the molecule moves translationally and rotationally into the condensate without any friction. In particular, we show that the rotational energy released by the molecule is large enough to eject one atom out of the condensate. The detection of such an atom provides a direct measurement of the low-energy cross section of the scattering with the rotating molecule. Finally, increases of inertia and of centrifugal distortion of the molecule due to the surrounding condensate are estimated and compared with the experimental data obtained for a He4 droplet.
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Power, W. L.
A1  - Pfau, T.
A1  - Wilkens, Martin
T1  - Loading atoms into a surface trap: simulations of an experimental scheme
N2  - We present simulations of a scheme for the continuous loading of pre-cooled atoms into the lowest energy states of an optical surface trap. The atoms fall under gravity towards the surface of a prism where evanescent waves are used to decelerate the falling atoms and to pump them into a trapped state in an optical standing wave. The simulations are performed using the Monte-Carlo wavefunction technique and are designed to represent the proposed experimental scheme as closely as is practically possible. The probabilities of atoms being pumped into the different trapped states have been calculated as a function of the properties of the braking and pumping fields. The effective temperature of the final distribution of the atoms is calculated in order to find the change in phase-space density.
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Power, W. L.
A1  - Tan, S. M.
A1  - Wilkens, Martin
T1  - A scheme for the simultaneous measurement of atomic position and momentum
N2  - We propose an optical scheme for the simultaneous measurement of the position and momentum of a single atom. The scheme involves the coupling of the atom of two light fields with different spatical and polarization characteristics. The proposed technique is closely related to the Arthurs-Kelly measurement scheme; the principal difference is that in the present case the electromagnetic fields rather than from shifts in the position of a pointer.
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Pu, Han
A1  - Zhang, Weiping
A1  - Wilkens, Martin
A1  - Meystre, Pierre
T1  - Phonon Spectrum and Dynamical Stability of a Dilute Quantum Degenerate Bose-Fermi Mixture
N2  - We calculate the phonon excistation spectrum in a zero-temperature dilute boson-fermion gaseous mixture. We show how the sound velocity changes due to the boson-fermion interaction, and we determine the dynamical stability regime of a homogeneous mixture. We identify a resonant phonon-exchange interaction between the fermions as the physical mechanism leading to the instability.
Y1  - 2002
ER  - 
TY  - JOUR
A1  - Raetzel, Dennis
A1  - Wilkens, Martin
A1  - Menzel, Ralf
T1  - Gravitational properties of light: The emission of counter-propagating laser pulses from an atom
JF  - Physical review : D, Particles, fields, gravitation, and cosmology
Y1  - 2017
U6  - https://doi.org/10.1103/PhysRevD.95.084008
SN  - 2470-0010
SN  - 2470-0029
VL  - 95
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Rzazewski, Kazimierz
A1  - Goral, K.
A1  - Cirone, M. A.
A1  - Wilkens, Martin
T1  - Bose-Einstein Condensation of two interacting particles
N2  - We investigate the notion of Bose-Einstein condensation of interacting particles. The definition of the condensate is based on the existence of the dominant eigenvalue of the single-particle density matrix. The statistical properies and the characteristics temperature are computed exactly in the soluble models of two interacting atoms.
Y1  - 2001
ER  - 
TY  - JOUR
A1  - Rätzel, Dennis
A1  - Wilkens, Martin
A1  - Menzel, Ralf
T1  - Effect of polarization entanglement in photon-photon scattering
JF  - Physical review : A, Atomic, molecular, and optical physics
N2  - It is found that the differential cross section of photon-photon scattering is a function of the degree of polarization entanglement of the two-photon state. A reduced general expression for the differential cross section of photon-photon scattering is derived by applying simple symmetry arguments. An explicit expression is obtained for the example of photon-photon scattering due to virtual electron-positron pairs in quantum electrodynamics. It is shown how the effect in this explicit example can be explained as an effect of quantum interference and that it fits with the idea of distance-dependent forces.
Y1  - 2017
U6  - https://doi.org/10.1103/PhysRevA.95.012101
SN  - 2469-9926
SN  - 2469-9934
VL  - 95
IS  - 1
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Rätzel, Dennis
A1  - Wilkens, Martin
A1  - Menzel, Ralf
T1  - Gravitational properties of light
BT  - the gravitational field of a laser pulse
JF  - New journal of physics : the open-access journal for physics
N2  - The gravitational field of a laser pulse of finite lifetime, is investigated in the framework of linearized gravity. Although the effects are very small, they may be of fundamental physical interest. It is shown that the gravitational field of a linearly polarized light pulse is modulated as the norm of the corresponding electric field strength, while no modulations arise for circular polarization. In general, the gravitational field is independent of the polarization direction. It is shown that all physical effects are confined to spherical shells expanding with the speed of light, and that these shells are imprints of the spacetime events representing emission and absorption of the pulse. Nearby test particles at rest are attracted towards the pulse trajectory by the gravitational field due to the emission of the pulse, and they are repelled from the pulse trajectory by the gravitational field due to its absorption. Examples are given for the size of the attractive effect. It is recovered that massless test particles do not experience any physical effect if they are co-propagating with the pulse, and that the acceleration of massless test particles counter-propagating with respect to the pulse is four times stronger than for massive particles
at rest. The similarities between the gravitational effect of a laser pulse and Newtonian gravity in two dimensions are pointed out. The spacetime curvature close to the pulse is compared to that induced by gravitational waves from astronomical sources.
KW  - gravity
KW  - general relativity
KW  - laser pulses
KW  - electromagnetic radiation
KW  - linearized gravity
KW  - pp-wave solutions
Y1  - 2016
U6  - https://doi.org/10.1088/1367-2630/18/2/023009
SN  - 1367-2630
VL  - 18
SP  - 1
EP  - 16
PB  - IOP Science
CY  - London
ER  - 
TY  - JOUR
A1  - Rätzel, Dennis
A1  - Wilkens, Martin
A1  - Menzel, Ralf
T1  - Gravitational properties of light-the gravitational field of a laser pulse
JF  - NEW JOURNAL OF PHYSICS
N2  - The gravitational field of a laser pulse of finite lifetime, is investigated in the framework of linearized gravity. Although the effects are very small, they may be of fundamental physical interest. It is shown that the gravitational field of a linearly polarized light pulse is modulated as the norm of the corresponding electric field strength, while no modulations arise for circular polarization. In general, the gravitational field is independent of the polarization direction. It is shown that all physical effects are confined to spherical shells expanding with the speed of light, and that these shells are imprints of the spacetime events representing emission and absorption of the pulse. Nearby test particles at rest are attracted towards the pulse trajectory by the gravitational field due to the emission of the pulse, and they are repelled from the pulse trajectory by the gravitational field due to its absorption. Examples are given for the size of the attractive effect. It is recovered that massless test particles do not experience any physical effect if they are co-propagating with the pulse, and that the acceleration of massless test particles counter-propagating with respect to the pulse is four times stronger than for massive particles at rest. The similarities between the gravitational effect of a laser pulse and Newtonian gravity in two dimensions are pointed out. The spacetime curvature close to the pulse is compared to that induced by gravitational waves from astronomical sources.
KW  - gravity
KW  - general relativity
KW  - laser pulses
KW  - electromagnetic radiation
KW  - linearized gravity
KW  - pp-wave solutions
Y1  - 2016
U6  - https://doi.org/10.1088/1367-2630/18/2/023009
SN  - 1367-2630
VL  - 18
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Rätzel, Dennis
A1  - Wilkens, Martin
A1  - Menzel, Ralf
T1  - The effect of entanglement in gravitational photon-photon scattering
JF  - epl : a letters journal exploring the frontiers of physics
N2  - The differential cross-section for gravitational photon-photon scattering calculated in perturbative quantum gravity is shown to depend on the degree of polarization entanglement of the two photons. The interaction between photons in the symmetric Bell state is stronger than between not entangled photons. In contrast, the interaction between photons in the anti-symmetric Bell state is weaker than between not entangled photons. The results are interpreted in terms of quantum interference, and it is shown how they fit into the idea of distance-dependent forces. Copyright (C) EPLA, 2016
Y1  - 2016
U6  - https://doi.org/10.1209/0295-5075/115/51002
SN  - 0295-5075
SN  - 1286-4854
VL  - 115
SP  - S12
EP  - S13
PB  - EDP Sciences
CY  - Mulhouse
ER  - 
TY  - JOUR
A1  - Stenholm, Stig
A1  - Wilkens, Martin
T1  - Jumps in quantum theory
N2  - In this paper we review the discussion about quantum jumps. We sketch the historical background before we present the recent revival of this problem originating in the field of atomic investigations. We present both the theoretical methods and their motivations, the relevance to experiments and an attempt at a preliminary discussion of the role of these developments in our fundamental understanding of quantum physics.
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Tino, G. M.
A1  - Cacciapuoti, L.
A1  - Bongs, K.
A1  - Bordé, Ch. J.
A1  - Bouyer, P.
A1  - Dittus, H.
A1  - Ertmer, W.
A1  - Görlitz, A.
A1  - Inguscio, M.
A1  - Landragin, A.
A1  - Lemonde, P.
A1  - Lämmerzahl, C.
A1  - Peters, A.
A1  - Rasel, E.
A1  - Reichel, J.
A1  - Salomon, C.
A1  - Schiller, S.
A1  - Schleich, W.
A1  - Sengstock, K.
A1  - Sterr, U.
A1  - Wilkens, Martin
T1  - Atom interferometers and optical atomic clocks : new quantum sensors for fundamental physics experiments in space
N2  - We present projects for future space missions using new quantum devices based on ultracold atoms. They will enable fundamental physics experiments testing quantum physics, physics beyond the standard model of fundamental particles and interactions, special relativity, gravitation and general relativity.
Y1  - 2007
ER  - 
TY  - JOUR
A1  - Weiss, Christoph
A1  - Wilkens, Martin
T1  - Particle number counting statistics in ideal Bose gases
N2  - We discuss the exact particle number counting statistics of degenerate ideal Bose gases in the microcanonical, canonical, and grand-canonical ensemble, respectively, for various trapping potentials. We then invoke the Maxwell's Demon ensemble [P. Navez et al., Phys. Rev. Lett.(1997)] and show that for large total number of particles the root-mean-square fluctuation of the condensate occupation scales delta n0 proportional to [T/Tc]r Ns with scaling exponents r=3/2, s=1/2 for the 3D harmonic oscillator trapping potential, and r=1, s=2/3 for the 3D box. We derive an explicit expression for r and s in terms of spatial dimension D and spectral index sigma of the single- particle energy spectrum. Our predictions also apply to systems where Bose-Einstein condensation does not occur. We point out that the condensate fluctuations in the microcanonical and canonical ensemble respect the principle of thermodynamic equivalence.
Y1  - 1997
UR  - http://epubs.osa.org/oearchive/source/2372.htm
ER  - 
TY  - JOUR
A1  - Wilkens, Martin
T1  - Quantum Phase of a Moving Dipole
N2  - It is shown that a neutral particle with an electric dipole moment which moves in a magnetic field acquires a topological phase. This phase may be observed in atom or molecular interferometry.
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Wilkens, Martin
T1  - AS TIME GOES BY. Rythmizität Zyklizität - Kategorien zeitlicher Stukturierung
JF  - Zyklizität & Rhythmik: eine multidisziplinäre Vorlesungsreihe
Y1  - 2020
SN  - 978-3-86464-169-5
SP  - 71
EP  - 84
PB  - trafo
CY  - Berlin
ER  - 
TY  - JOUR
A1  - Wilkens, Martin
A1  - Illuminati, Fabrizio
A1  - Krämer, Meret
T1  - Transition temperature of the weakly interacting Bose gas: perturbative solution of the crossover equations in the canonical ensemble
N2  - We compute the shift of the critical temperature Tc with respect to the ideal case for a weakly interacting uniform Bose gas. We work in the framework of the canonical ensemble, extending the criterion of condensation provided by the canonical particle counting statistics for the zero-momentum state of the uniform ideal gas. The perturbative solution of the crossover equation to lowest order in power of the scattering length yields (Tc - Tc0)/Tc0=-0,93ap 1/3, where Tc0 is the transition temperature of the corresponding ideal Bose gas , a is the scattering length, and p is the particle number density. This is at vaiance with the standard grand canonical prediction of a null shift of the critical temperature in the lowest perturbative order. The non-equevalence of statistical ensemble for the ideal Bose gas is thus confirm (at the lowestperturbative level) also in the presence of interactions.
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Wilkens, Martin
A1  - Weiss, Christoph
T1  - Particle number fluctuations in an ideal Bose gas
N2  - We analyse occupation number fluctuations of an ideal Bose gas in a trap which is isolated from theenvironment with respect to particle exchange (canonical ensemble). We show that in contrast to the predictions of thegrand- canonical ensemble, the counting statistics of particles in the trap ground state changes from monotonously decreasing above the condensation temperature to single-peaked below that temperature. For the exactly solvable case of a harmonic oscillator trapping potential in one spatial dimension we extract a Landau-Ginzburg functional which - despite the non- interacting nature of the system - displays the characteristic behaviour of a weakly interacting Bose gas. We also compare our findings with the usual treatment which is base on the grand-canonical ensemble. We show that for an ideal Bose gas neither are the grand-canonical and canonical ensemble thermodynamically equivalent, nor the grand-canonical ensemble can be viewed as a small system in diffusive contact with a particle reservoir.
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Öhberg, P.
A1  - Surkov, E. L.
A1  - Tittonen, I.
A1  - Stenholm, Stig
A1  - Wilkens, Martin
A1  - Shlyapnikov, G. V.
T1  - Low-energy elementary excitations of a trapped Bose-condensed gas
N2  - We develop a method of finding analytical sotutions of the Bogolyubov-de Gennes equations for the excitations of a Bose condensate in the Thomas-Fermi regime in harmonic traps of any asymmetry and introduce a classification of eigenstates. In the case of cylindrical symmetry we emphasize the presence of an accidental degeneracy in the excitation spectrum at certain values of the projection of orbital angular momentum on the symmetry axis and discuss possible consequences of the degeneracy in the context of new signatures of Bose- Einstein condensation
Y1  - 1997
ER  -